Some cancers are exquisitely sensitive to anti-cancer treatment. For example, patients whose lung adenocarcinomas harbor specific mutations in the epidermal growth factor receptor (EGFR) tyrosine kinase domain frequently experience clinical and radiographic responses to the selective EGFR tyrosine kinase inhibitors (TKIs) gefitinib (Iressa) and eriotinib (Tarceva). Medulloblastomas analogously are extremely sensitive to radiation treatment. However, in both instances, the disease returns. In half of such lung cancer patients, the Pao Lab has demonstrated that tumor cells harbor a second mutation in the EGFR kinase domain, which alters a 'gatekeeper' residue (T790M) in the ATP-binding pocket. In patients with medulloblastoma, data from the Holland Lab suggests that radiation-resistant cells in the perivascular niche undergo Gl arrest in response to treatment and then self-renew, giving rise to recurrence. Since acquired resistance to represent severe limitations, and since existing treatment schedules were established empirically, we propose an interdisciplinary approach utilizing mathematical modeling and unique experimental systems to predict and prevent the emergence of resistance against targeted drugs and radiation therapy. We have already developed a mathematical framework for the general scenario of drug resistance emerging during therapy with targeted drugs. We now will: 1) broaden the mathematical framework to include more complex scenarios in cancer therapy; 2) apply the models to minimize the risk of resistance to EGFR TKIs in lung cancer, using quantitative measurements obtained from appropriate isogenic cell lines and in vivo transgenic lung tumor models; 3) apply the models to minimize the risk of resistance to radiation in medulloblastoma, using quantitative measurements obtained from a novel transgenic mouse model Collectively, these studies will lead to the rational design of clinical trials to prevent the emergence of resistance. This project is multi-institutional (Vanderbilt and MSKCC), cross-disciplinary, and will rely upon physical measurements obtained from the PS-OC Core (Altan-Bonnet).